There is nothing harder, physically and emotionally, than having a dog aggressive dog (well maybe a dog and human aggressive dog).
Every walk and outside experience is stressful and it is very very hard to at times not hold it against the dog.
You do have your hands full but it is not my position to judge you on the sense of it.
What are your options?
Get some outside help - maybe a dog walker a few times a week to give you more time or a trainer to help with the dogs
Rehome the dogs - the chances for the 10 yr old are not good if he has issues and also older will not likely to get rehomed - however if he was a rescue I would speak to the rescue centre for advice.
Have a break - can you put the dogs in kennels for a weekend recharge, regroup and then try again.
Do ask for help - can some of the other daily tasks be shared so you are not so stretched.
Owning a dog is hard work, owning an aggressive dog is very very hard and unless people have been there they can not understand the strain that it has on a family. Puppies are very hard work and relentless.
As the puppy gets older this will make things much easier and hopefully good dog will rub off on the puppy so you have two good dogs and an elderly dog that just needs a bit of love and care.